\section{Imaginary and Complex Numbers}

Lasses dokument no longer used

An imaginary number, is a number that when squared, gives a negative number. Opposite to real numbers that can only result in a positive numbers when squared (or 0).
 
E.g. (2 * 2 = 4), but so does (-2 * -2 = 4).

With imaginary numbers, one has to imagine that a number squared can result in a negative number. Imaginary numbers are often denoted \textit{i} for imaginary. The definition of \textit{i} is:

\textit{i} * \textit{i} = -1

\textit{i} raised to different powers only have four results:

\begin{figure}[htbp]
\centering
\includegraphics[width=0.7\textwidth]{images/ImaginaryComplex/TesterTilLatex.png}
\caption*{}
\label{fig:IRaised}
\end{figure}
To show that these four numbers keep cycling no matter how big the exponent is, let us take some examples:

\begin{figure}[htbp]
\centering
\includegraphics[width=0.3\textwidth]{images/ImaginaryComplex/TesterTilLatex1}
\caption*{}
\label{fig:IRaised1}
\end{figure}

If the above equation is true, then the following equation is also true:

\centering$i=\sqrt{-1}$
\
Let us take an example of dealing with a complex square root function:

\begin{equation}
simplify: \sqrt{-52}
\end{equation}


